Apparatus having an array of piezoelectric film sensors for measuring parameters of a process flow within a pipe

ABSTRACT

A apparatus  10,110,170  is provided that measures the speed of sound and/or vortical disturbances propagating in a single phase fluid flow and/or multiphase mixture to determine parameters, such as mixture quality, particle size, vapor/mass ratio, liquid/vapor ratio, mass flow rate, enthalpy and volumetric flow rate of the flow in a pipe, by measuring acoustic and/or dynamic pressures. The apparatus includes a spatial array of unsteady pressure sensors  15 - 18  placed at predetermined axial locations x 1 -x N  disposed axially along the pipe  14 . The pressure sensors  15 - 18  provide acoustic pressure signals P 1 (t)-P N (t) to a signal processing unit  30  which determines the speed of sound a mix  propagating through of the process flow  12  flowing in the pipe  14 . The pressure sensors are piezoelectric film sensors that are mounted or clamped onto the outer surface of the pipe at the respective axial location.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/425,436 (Cidra Docket No. CC-0538), filed Nov. 12,2002; and U.S. Provisional Application No. 60/426,724 (Cidra Docket No.CC-0554), filed Nov. 15, 2002, all of which are incorporated herein byreference in their entirety.

TECHNICAL FIELD

[0002] This invention relates to an apparatus for measuring theparameters of a single phase and/or multiphase flow, and moreparticularly to an apparatus having an array of piezoelectric filmsensors clamped or mounted onto a process flow pipe for measuring thespeed of sound and/or vortical disturbances propagating in a singlephase and/or multiphase flow to determine parameters, such as mixturequality, particle size, vapor/mass ratio, liquid/vapor ratio, mass flowrate, enthalpy and volumetric flow rate of the flow in the pipe, forexample, by measuring acoustic and/or dynamic pressures.

BACKGROUND ART

[0003] Numerous technologies have been implemented to measure volumetricand mass flow rates of fluids in industrial processes. Some of the morecommon approaches are based upon ultrasonic time of flight and/orDoppler effects, Coriolis effects, rotating wheels, electromagneticinduction, and pressure differentials. Each of these techniques hascertain drawbacks. For example, invasive techniques that rely oninsertion of a probe into the flow, or geometry changes in the pipe, maybe disruptive to the process and prone to clogging. Other methods suchas ultrasonics may be susceptible to air or stratified flow. Meters thatuse rotating wheels or moving parts are subject to reliability issues.Coriolis meters are limited when pipe diameters become large due to theincrease in force required to vibrate the pipe.

[0004] One such process fluid is a saturated vapor/liquid fluid mixture(e.g., steam). It would be advantageous to be able to measure the vaporquality of this fluid mixture. Vapor quality of a saturated vapor/liquidmixture is defined as ratio of the mass of the vapor phase to the totalmass of the mixture. Saturated mixtures exist at temperatures andpressures at which liquid and vapor phases coexist. The temperatures andpressures at which the liquid and vapor phases coexist lie under the“vapor bubble” on a phase diagram. The collection of points known as thesaturated liquid line and the collections of points known as thesaturated vapor line define the vapor bubble. These two lines connectat, what is termed, the critical point. Saturated mixtures exist onlyunder the vapor bubble. For pressures and temperatures outside of thevapor bubble, the fluid exists as a single phase and the properties ofthat fluid, such as density, enthalpy, internal energy, etc., areuniquely defined by the pressure and temperature. For common fluids,such as water, these properties are tabulated as functions of pressureand temperatures and are available through a variety of referencesincluding a website hosted by NIST (ref:http://webbook.nist.gov/chemistr/fluid/).

[0005] For fluids at pressures and temperatures that lie within thevapor bubble, the fluids represent mixtures of the liquid and vaporphase. Although the properties of both the vapor and liquid phases arewell defined (and tabulated for known substances), the properties of themixture are no longer uniquely defined as functions of pressure andtemperature. In order to define the averaged properties of a saturatedmixture, the ratio of the vapor and liquid components of the mixturemust be defined. The quality of the mixture, in addition to the pressureand temperature, must be defined to uniquely determine the properties ofthe mixture.

[0006] Measuring the average properties of a single or multi-phaseprocess flow is important in many industrial application since it is themass averaged properties of the working fluid that enter directly intomonitoring the thermodynamic performance of many processes. For example,it is the difference in the flux of enthalpy of the steam mixtureflowing into and exiting from a turbine that determines the maximummechanical work that can be extracted from the working fluid, and thusis critical to determining component efficiency. However, if the steamentering or exiting the turbine were saturated, pressure and temperaturemeasurement would not sufficient to determine the specific enthalpy, butrather, a measure of the quality of the steam would be required touniquely define the thermodynamic properties of the saturated steammixture.

[0007] Note that once the quality and pressure (or temperature) of asaturated mixture is defined, the thermodynamic properties of themixture are defined through mixing laws provided the properties of theliquid and vapor sates are known. For example, measuring speed of soundenables one to determine quality, which in turn enables one to calculateenthalpy, density, and other properties of the mixture. In addition tomeasuring the specific enthalpy, a measurement of the total mass isalso, in general, required to determine the flux of enthalpy.

[0008] There are many other situations where knowing the quality of asaturated mixture is beneficial. For example, in a steam power plant,the quality of the steam within the steam turbine affects blade life.Generally it is desired to operate so the quality is as high as possiblethroughout the turbine to minimize liquid water drops that will erodethe metal blades. Knowing the quality at the turbine inlet and exhaust(or at the exhaust only if the inlet is super-heated) provides a meansto monitor the quality throughout the turbine. Also, to monitor plantperformance so that it can be operated at optimum conditions and toidentify degradation effects, the steam turbine thermal performance mustbe known. This requires the fluid enthalpy at the inlet and exhaust ofeach turbine to be known. If the fluid at either or both locations issaturated, pressure and temperature measurements alone will not beenough to determine the enthalpy. However if an additional measurementof quality is made the enthalpy is then defined. In addition, there maybe other applications in refrigeration cycles.

[0009] The ability to measure the flow rate and composition of thesaturated vapor/liquid mixtures within the conduits is an importantaspect of any system or strategy design to optimize the performance of asystem based on saturated vapor/liquid mixtures. The industry recognizesthis, and has been developing a wide variety of technologies to performthis measurement. These include probe based devices, sampling devices,venturis and ultrasonic devices

[0010] This invention provides an apparatus and method to measurehomogeneous and/or non-homogeneous fluids used in industrial systemshaving various working fluids to determine various parameters of theprocess fluid, such as the volumetric flow of the fluid, the consistencyor composition of the fluid, the density of the fluid, the Mach numberof the fluid, the size of particle flowing through the fluid, theair/mass ratio of the fluid and/or the percentage of entrained air/gaswithin a liquid or slurry.

[0011] Here a novel approach to flow measurements is proposed whichutilizes a non-intrusive, externally mounted sensing element thatrequires no moving parts and is highly reliable. This approach is basedupon signal correlation and/or array processing techniques of unsteadypressure measurements induced in an array of externally mounted sensors.The piezo-film sensors clamped onto the outer surface of a pipe providescircumferential averaging of the unsteady pressures within the pipe andprovide an inexpensive solution to accurately measuring the unsteadypressures. The piezo-film also have the advantage of being able to wraparound a substantial portion of the outer circumference of the pipe toprovide circumferential averaging of the unsteady pressures with thepipe.

SUMMARY OF THE INVENTION

[0012] Objects of the present invention include an apparatus having anarray of piezoelectric film sensors mounted or clamped axially spaced tothe outer surface of the pipe for measuring the unsteady pressures of asingle and multi-phase process flows within a pipe to determine at leastone parameter of the process flow.

[0013] According to the present invention, an apparatus for measuring atleast one parameter of a process flow flowing within a pipe. Theapparatus includes at least two pressure sensors disposed on the outersurface of the pipe at different axial locations along the pipe. Each ofthe pressure sensors provides a respective pressure signal indicative ofa pressure disturbance within the pipe at a corresponding axialposition. Each of the pressure sensors includes a piezoelectric filmsensor. A signal processor, responsive to said pressure signals,provides a signal indicative of at least one parameter of the processflow flowing within the pipe.

[0014] The foregoing and other objects, features and advantages of thepresent invention will become more apparent in light of the followingdetailed description of exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015]FIG. 1a schematic illustration of an apparatus having an array ofpiezoelectric film sensors clamped onto the outer surface a pipe, inaccordance with the present invention.

[0016]FIG. 1b is a schematic illustration of an apparatus having anarray of piezoelectric film sensors mounted on the outer surface of apipe, in accordance with the present invention.

[0017]FIG. 2 is a cross-sectional view of a pipe and array of sensorsshowing the turbulent structures within the pipe, in accordance with thepresent invention.

[0018]FIG. 3 is a cross-sectional view of a piezoelectric film sensor inaccordance with the present invention.

[0019]FIG. 4 is a top plan view of a piezoelectric film sensor inaccordance with the present invention.

[0020]FIG. 5 is a cross-sectional view of a portion of the piezoelectricfilm sensor and clamp, in accordance with the present invention.

[0021]FIG. 6 is a cross-sectional view of a portion of the piezoelectricfilm sensor and clamp, in accordance with the present invention.

[0022]FIG. 7 is a cross-sectional view of a portion of the piezoelectricfilm sensor and clamp, in accordance with the present invention.

[0023]FIG. 8 is a side elevational view of a portion of thepiezoelectric film sensor and clamp showing a step in the attachment ofthe clamp to the pipe, in accordance with the present invention.

[0024]FIG. 9 is a side elevational view of a portion of thepiezoelectric film sensor and clamp, in accordance with the presentinvention.

[0025]FIG. 10 is a perspective view of a plurality of piezoelectric filmsensors clamped to a pipe having covers disposed thereover, inaccordance with the present invention.

[0026]FIG. 11 is a cross sectional end view of a piezoelectric filmsensor clamped to a pipe, in accordance with the present invention.

[0027]FIG. 12 is a block diagram of a probe for measuring the speed ofsound propagating through a process flow flowing within a pipe, inaccordance with the present invention.

[0028]FIG. 13 is a plot showing the standard deviation of sound speedversus frequency for various arrays of process flow parametermeasurement system, in accordance with the present invention.

[0029]FIG. 14 is a kω plot of data processed from an array of pressuresensors use to measure the speed of sound propagating through asaturated vapor/liquid mixture flowing in a pipe, in accordance with thepresent invention.

[0030]FIG. 15 is a block diagram of an apparatus for measuring thevortical field of a process flow within a pipe, in accordance with thepresent invention.

[0031]FIG. 16 is a kω plot of data processed from an apparatus embodyingthe present invention that illustrates slope of the convective ridge,and a plot of the optimization function of the convective ridge, inaccordance with the present invention.

[0032]FIG. 17 is a functional flow diagram of an apparatus embodying thepresent invention.

BEST MODE FOR CARRYING OUT THE INVENTION

[0033] Referring to FIG. 1a, an apparatus, generally shown as 10, isprovided to sense and determine specific characteristics or parametersof a single phase fluid 12 (e.g., gas and liquid) and/or a multi-phasemixture 12 (e.g., process flow) flowing through a pipe. The multi-phasemixture may be a two-phase liquid/vapor mixture, a solid/vapor mixtureor a solid/liquid mixture, gas entrained liquid or even a three-phasemixture. As will be described in greater detail, the apparatus measuresthe speed of sound propagating through the fluid or multiphase mixtureflow to determine any one of a plurality of parameters of the flow, suchas the steam quality or “wetness”, vapor/mass ratio, liquid/solid ratio,the volumetric flow rate, the mass flow rate, the size of the suspendedparticles, density, gas volume fraction, and the enthalpy of the flow.Additionally, the apparatus 10 is capable of measuring the unsteadypressure disturbances (e.g., vortical effects, density changes) of theflow passing through the pipe to determine the velocity of the flow, andhence the volumetric flow rate of the flow.

[0034]FIG. 1a illustrates a schematic drawing of the apparatus 10 thatincludes a sensing device 16 comprising an array of pressure sensors (ortransducers) 18-21 spaced axially along the outer surface 22 of a pipe14, having a process flow propagating therein. The pressure sensorsmeasure the unsteady pressures produced by acoustical and/or vorticaldisturbances within the pipe, which are indicative of a parameter of thesingle phase fluid or multiphase mixture 12. The output signals (P₁-P₄)of the pressure sensors 18-21 are provided to a processing unit 24,which processes the pressure measurement data and determines at leastone parameter of the flow. Such as, the characteristics and parametersdetermined may include the volumetric flow of the flow, the consistencyor composition of the flow, the density of the mixture, the Mach numberof the flow, the size of particle flowing through the mixture, theair/mass ratio of the mixture and/or the percentage of entrained air orgas within the mixture.

[0035] In an embodiment of the present invention shown in FIG. 1a, theapparatus 10 has four pressure sensors 18-21 disposed axially along thepipe 14 for measuring the unsteady pressure P₁-P₄ of the fluid ormixture 12 flowing therethrough. The apparatus 10 has the ability tomeasure the volumetric flow rate and other flow parameters using one orboth of the following techniques described herein below:

[0036] 1) Determining the speed of sound of acoustical disturbances orsound waves propagating through the flow 12 using the array of pressuresensors 18-21, and/or

[0037] 2) Determining the velocity of vortical disturbances or “eddies”propagating through the flow 12 using the array of pressure sensors18-21.

[0038] Generally, the first technique measures unsteady pressurescreated by acoustical disturbances propagating through the flow 12 todetermine the speed of sound (SOS) propagating through the flow. Knowingthe pressure and/or temperature of the flow and the speed of sound ofthe acoustical disturbances, the processing unit 24 can determine themass flow rate, the consistency of the mixture (i.e., the mass/airratio, the mass/liquid ratio, the liquid/air ratio), the volumetric flowrate, the density of the mixture, the enthalpy of the mixture, the Machnumber of the mixture, the size of the particles within a mixture, andother parameters, which will be described in greater detail hereinafter.

[0039] The apparatus in FIG. 1a also contemplates providing one or moreacoustic sources 27 to enable the measurement of the speed of soundpropagating through the flow for instances of acoustically quiet flow.The acoustic sources may be disposed at the input end of output end ofthe probe, or at both ends as shown. One should appreciate that in mostinstances the acoustics sources are not necessary and the apparatuspassively detects the acoustic ridge provided in the flow 12.

[0040] The second technique measures the velocities associated withunsteady flow fields and/or pressure disturbances created by vorticaldisturbances or “eddies” 118 to determine the velocity of the flow 12.The pressure sensors 18-21 measure the unsteady pressures P₁-P₄ createdby the vortical disturbances as these disturbances convect within theflow 12 through the pipe 14 in a known manner, as shown in FIG. 2.Therefore, the velocity of these vortical disturbances is related to thevelocity of the mixture and hence the volumetric flow rate may bedetermined, as will be described in greater detail hereinafter.

[0041] In one embodiment of the present invention as shown in FIGS. 1a,1 b and 2, each of the pressure sensors 18-21 may include apiezoelectric film sensor 30 as shown in FIGS. 3 and 4 to measure theunsteady pressures of the mixture 12 using either technique describedhereinbefore.

[0042] As best shown in FIGS. 3 and 4, the piezoelectric film sensors 30include a piezoelectric material or film 32 to generate an electricalsignal proportional to the degree that the material is mechanicallydeformed or stressed. The piezoelectric sensing element is typicallyconformed to allow complete or nearly complete circumferentialmeasurement of induced strain to provide a circumferential-averagedpressure signal. The sensors can be formed from PVDF films, co-polymerfilms, or flexible PZT sensors, similar to that described in “Piezo FilmSensors Technical Manual” provided by Measurement Specialties, Inc.,which is incorporated herein by reference. A piezoelectric film sensorthat may be used for the present invention is part number 1-1002405-0,LDT4-028K, manufactured by Measurement Specialties, Inc.

[0043] Piezoelectric film (“piezofilm”), like piezoelectric material, isa dynamic material that develops an electrical charge proportional to achange in mechanical stress. Consequently, the piezoelectric materialmeasures the strain induced within the pipe 14 due to unsteady pressurevariations (e.g., vortical and/or acoustical) within the process mixture12. Strain within the pipe is transduced to an output voltage or currentby the attached piezoelectric sensor. The piezoelectrical material orfilm may be formed of a polymer, such as polarized fluoropolymer,polyvinylidene fluoride (PVDF).

[0044]FIGS. 3 and 4 illustrate a piezoelectric film sensor (similar tothe sensor 18 of FIG. 1a), wherein the piezoelectric film 32 is disposedbetween and pair of conductive coatings 34,35, such as silver ink. Thepiezoelectric film 32 and conductive coatings 34,35 are coated onto aprotective sheet 36 (e.g., mylar) with a protective coating 38 disposedon the opposing side of the upper conductive coating. A pair ofconductors 40,42 is attached to a respective conductive coating 34,35.

[0045] The thickness of the piezoelectric film 32 may be in the range of8 um to approximately 110 um. The thickness is dependent on the degreeof sensitivity desired or needed to measure the unsteady pressureswithin the pipe 14. The sensitivity of the sensor 30 increases as thethickness of the piezoelectric film increases.

[0046] The advantages of this technique of clamping the PVDF sensor 30onto the outer surface of the pipe 14 are the following:

[0047] 1. Non-intrusive flow rate measurements

[0048] 2. Low cost

[0049] 3. Measurement technique requires no excitation source. Ambientflow noise is used as a source.

[0050] 4. Flexible piezoelectric sensors can be mounted in a variety ofconfigurations to enhance signal detection schemes. These configurationsinclude a) co-located sensors, b) segmented sensors with opposingpolarity configurations, c) wide sensors to enhance acoustic signaldetection and minimize vortical noise detection, d) tailored sensorgeometries to minimize sensitivity to tube modes, e) differencing ofsensors to eliminate acoustic noise from vortical signals.

[0051] 5. Higher Operating Temperatures (125 C.) (co-polymers)

[0052] Referring to FIG. 1b, the piezoelectric film sensors 30 may bemounted directly onto the outer diameter of the pipe 14 by epoxy, glueor other adhesive.

[0053] Alternatively, as shown in FIGS, 5-9, the piezoelectric filmsensor 30 is be adhered or attached to a strap 72 which is then clamped(or strapped) onto the outer surface of the pipe 14 at each respectiveaxial location, similar to that described in U.S. ProvisionalApplication No. 60/425,436 (Cidra Docket No. CC-0538), filed Nov. 12,2002; and U.S. Provisional Application No. 60/426,724 (Cidra Docket No.CC-0554), which are incorporated herein by reference.

[0054] As shown in FIG. 5, the piezoelectric film sensor 30 is attachedto the outer surface 73 of the strap in relation to the pipe 14. Theconductive insulator 36 is attached to the outer surface of the strap bydouble side tape or any other appropriate adhesive. The adhesive ispreferably flexible or compliant but minimizes creep between the strapand piezoelectric film sensor during the operation of the sensor 30. Thelength of the strap is substantially the same as the circumference ofthe pipe 14. The piezoelectric film sensor may extend over thesubstantial length of the strap or some portion less than the strap. Inthe embodiment shown in FIG. 5, the piezoelectric film sensor 30 extendssubstantially the length of the strap 72 to provide a circumferentiallyaveraged pressure signal to the processing unit 24.

[0055] Referring to FIGS. 6 and 7, an attachment assembly 75 comprisinga first attachment block 76, a second attachment block 77 and a spacer78 disposed therebetween, which are welded together to provide slots 79between each of the attachment blocks and the spacer. The slots receiverespective ends of the strap 72 to secure the ends of the straptogether. One end of the strap 72 and the pair of conductors 40,42 arethreaded through the slot disposed between the first attachment blockand the spacer. The strap 72 and conductors 40,42 are secured to theattachment assembly by a pair of fasteners 80. The other end of thestrap is threaded through the slot disposed between the spacer and thesecond attachment block. Referring to FIG. 8, the other end of the strapis pull tightly between the spacer and the second attachment to draw upand take-up the tension and securely clamp the strap to the pipe 14. Asshown in FIG. 9, a set screw 81 within the second attachment block istighten, which then pierces the other end of the strap to secure it tothe attachment assembly. The excess portion of the other end of thestrap is then cut off. The piezoelectric film sensor may then be coveredwith a copper sheet to provide a grounding shield for EMI or otherelectrical noise.

[0056] While the piezoelectric film sensor 30 was mounted to the outersurface of the straps 72, the present invention contemplates thepiezoelectric film sensor may be mounted to the inner surface of thestrap, thereby resulting in the piezoelectric sensor being disposedbetween the strap and the outer surface of the pipe 14.

[0057]FIG. 10 illustrates a protective cover 82, having two halves,clamped onto the pipe and secured together over each of thepiezoelectric film sensors 30 and straps 72. The protective cover isformed from aluminum with thermal fins 83 molded therein to assist withdissipating heat away from the sensors. The cover further includes aninsulative portion 84 disposed between the pipe and the aluminum portionof the cover. The conductors and wiring thereto pass through a conduit84 that extends between each of the covers.

[0058] While the present invention illustrates separate covers for eachsensor, the present invention contemplates a single cover that coversall the sensors.

[0059] Referring to FIGS. 13 and 14, an apparatus 110, similar toapparatus 10 of FIG. 1a, embodying the present invention is providedthat measures at least one parameter/characteristic of a single and/ormultiphase flow 12 flowing within a pipe 14. The apparatus may beconfigured and programmed to measure the speed of sound propagatingthrough the flow 12 or measure the vortical disturbances propagatingthrough the flow 12. In some instances, the apparatus 10 may beconfigured to measure both the speed of sound and the vorticaldisturbances. Depending on the configuration or embodiment, theapparatus can measure at least one of the following parameters of theflow 12: the wetness or steam quality (volumetric phase fraction), thevolumetric flow rate, the size of the liquid particles, the mass flow,the enthalpy and the velocity of the mixture. To determine any one ofthese parameters, the apparatus 1 10 measures the unsteady pressurescreated by the speed of sound (SOS) and/or the vortical disturbancespropagating through the single phase or multiphase flow 12 flowing inthe pipe 14, which will be described in greater detail hereinafter.

[0060] The type of unsteady pressure measurement being made determinesthe spacing of the sensors. Measurement of unsteady vortical pressuresrequire sensors spacing less than the coherence length of the vorticaldisturbances which is typically on the order of a pipe diameter.Correlation or array processing of the unsteady vortical pressuremeasurements between sensors is used to determine the bulk flow rate ofthe process mixture, which will be described in greater detailhereinafter.

[0061] Mass flow rates and other parameters are determined by measuringthe speed of sound propagating within the process mixture 12. Theseparameters are determined by correlating or array processing unsteadypressure variations created by acoustic disturbances within the processmixture. In this case, the wavelength of the measured acoustic signaldetermines the sensor spacing. The desired wavelength of the measuredacoustic signal is dependent upon the dispersion of particles in themixture flow, which is dependent on the particle size. The larger theparticle size is the longer the sensing device of the aperture.

[0062] As described hereinbefore, the apparatus 110 of the presentinvention may be configured and programmed to measure and process thedetected unsteady pressures P₁(t)-P_(N)(t) created by acoustic wavesand/or vortical disturbances, respectively, propagating through themixture to determine parameters of the mixture flow 12. One suchapparatus 10 is shown in FIG. 12 that measures the speed of sound (SOS)of one-dimensional sound waves propagating through the vapor/liquidmixture to determine the composition the mixture. The apparatus 110 isalso capable of determining the average size of the droplets, velocityof the mixture, enthalpy, mass flow, steam quality or wetness, density,and the volumetric flow rate of the single or multi-phase flow 12. It isknown that sound propagates through various mediums at various speeds insuch fields as SONAR and RADAR fields. The speed of sound propagatingthrough the flow 12 within the pipe 14 may be determined using a numberof known techniques, such as those set forth in U.S. patent applicationSer. No. 09/344,094, entitled “Fluid Parameter Measurement in PipesUsing Acoustic Pressures”, filed Jun. 25, 1999, now U.S. Pat. No.6,354,147; U.S. patent application Ser. No. 09/729,994, filed Dec. 4,2002, now U.S. Pat. No. 6,609,069; and U.S. patent application Ser. No.10/007,749, entitled “Fluid Parameter Measurement in Pipes UsingAcoustic Pressures”, filed Nov. 7, 2001, each of which are incorporatedherein by reference.

[0063] In accordance with the present invention, the speed of soundpropagating through the process flow 12 is measured by passivelylistening to the flow with an array of unsteady pressure sensors todetermine the speed at which one-dimensional compression waves propagatethrough the flow 12 contained within the pipe 14.

[0064] As shown in FIG. 13, the apparatus 110 has an array of at leastthree acoustic pressure sensors 115,116,117, located at three locationsx₁,x₂,x₃ axially along the pipe 14. One will appreciate that the sensorarray may include more than three pressure sensors as depicted bypressure sensor 118 at location x_(N). The pressure generated by theacoustic waves may be measured through pressure sensors 115-118. Thepressure sensors 15-18 provide pressure time-varying signalsP₁(t),P₂(t),P₃(t),P_(N)(t) on lines 120,121,122,123 to a signalprocessing unit 130 to known Fast Fourier Transform (FFT) logics126,127,128,129, respectively. The FFT logics 126-129 calculate theFourier transform of the time-based input signals P₁(t)-P_(N)(t) andprovide complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω),P_(N)(ω) on lines 132,133,134,135 indicative of thefrequency content of the input signals. Instead of FFT's, any othertechnique for obtaining the frequency domain characteristics of thesignals P₁(t)-P_(N)(t), may be used. For example, the cross-spectraldensity and the power spectral density may be used to form a frequencydomain transfer functions (or frequency response or ratios) discussedhereinafter.

[0065] The frequency signals P₁(ω)-P_(N)(ω) are fed to a_(mix)-MxCalculation Logic 138 which provides a signal to line 40 indicative ofthe speed of sound of the multiphase mixture a_(mix) (discussed morehereinafter). The a_(mix) signal is provided to map (or equation) logic142, which converts a_(mix) to a percent composition of a mixture andprovides a % Comp signal to line 44 indicative thereof (as discussedhereinafter). Also, if the Mach number Mx is not negligible and isdesired, the calculation logic 138 may also provide a signal Mx to line46 indicative of the Mach number Mx.

[0066] More specifically, for planar one-dimensional acoustic waves in ahomogenous mixture, it is known that the acoustic pressure field P(x,t)at a location x along the pipe 14, where the wavelength λ of theacoustic waves to be measured is long compared to the diameter d of thepipe 14 (i.e., λ/d>>1), may be expressed as a superposition of a righttraveling wave and a left traveling wave, as follows:

P(x,t)=(Ae ^(−ik) ^(_(r)) ^(x) +Be ^(+ik) ^(_(l)) ^(x))e ^(iωt)  Eq. 1

[0067] where A,B are the frequency-based complex amplitudes of the rightand left traveling waves, respectively, x is the pressure measurementlocation along a pipe 14, o) is frequency (in rad/sec, where ω=2πf), andk_(r),k₁ are wave numbers for the right and left traveling waves,respectively, which are defined as: $\begin{matrix}{k_{r} \equiv {\left( \frac{\omega}{a_{mix}} \right)\frac{1}{1 + M_{x}}\quad {and}\quad k_{l}} \equiv {\left( \frac{\omega}{a_{mix}} \right)\frac{1}{1 - M_{x}}}} & {{Eq}.\quad 2}\end{matrix}$

[0068] where a_(mix) is the speed of sound of the mixture in the pipe, ωis frequency (in rad/sec), and M_(x), is the axial Mach number of theflow of the mixture within the pipe, where: $\begin{matrix}{M_{x} \equiv \frac{V_{mix}}{a_{mix}}} & {{Eq}.\quad 3}\end{matrix}$

[0069] where Vmix is the axial velocity of the mixture. Fornon-homogenous mixtures, the axial Mach number represents the averagevelocity of the mixture and the low frequency acoustic field descriptionremains substantially unaltered.

[0070] The data from the array of sensors 115-118 may be processed inany domain, including the frequency/spatial domain, the temporal/spatialdomain, the temporal/wave-number domain or the wave-number/frequency(k-ω) domain. As such, any known array processing technique in any ofthese or other related domains may be used if desired, similar to thetechniques used in the fields of SONAR and RADAR.

[0071] Also, some or all of the functions within the signal processingunit 130 may be implemented in software (using a microprocessor orcomputer) and/or firmware, or may be implemented using analog and/ordigital hardware, having sufficient memory, interfaces, and capacity toperform the functions described herein.

[0072] Acoustic pressure sensors 115-118 sense acoustic pressure signalsthat, as measured, are lower frequency (and longer wavelength) signalsthan those used for ultrasonic probes of the prior art, and thus thecurrent invention is more tolerant to inhomogeneities in the flow, suchas time and space domain inhomogeneities within the flow.

[0073] It is within the scope of the present invention that the pressuresensor spacing may be known or arbitrary and that as few as two sensorsare required if certain information is known about the acousticproperties of the process flow 12. The pressure sensors are spacedsufficiently such that the entire length of the array (aperture) is atleast a significant fraction of the measured wavelength of the acousticwaves being measured. The acoustic wavelength to be measured in amixture is a function of at least the size and mass of thedroplets/particles, and the viscosity of the vapor. The greater the sizeand mass of the droplets and/or the less viscous the vapor, the greaterthe spacing of the sensors is needed. Conversely, the smaller the sizeand mass of the droplets/particles and/or the more viscous the vapor,the shorter the spacing of the sensors is needed. For single phase flow,the acoustic wavelength is a function of the type or characteristics offlow 12.

[0074] Assuming that the droplets/particles of the mixture are smallenough and the acoustic frequencies and the frequencies of perturbationsassociated with the acoustics are low enough for the droplets/particlesof liquid to exhibit negligible slip (both steady and unsteady), thesound speed can be assumed to be substantially non-dispersive (that isconstant with frequency) and the volumetric phase fraction of themixture could be determined through the Wood equation:$\rho_{mix}{\sum\limits_{i = 1}^{N}{\varphi_{i}\rho_{i}}}$$\frac{1}{\rho_{mix}a_{mix}^{2}} = {\sum\limits_{i = 1}^{N}\frac{\varphi_{i}}{\rho_{i}a_{i}^{2}}}$${\sum\limits_{i = 1}^{N}\varphi_{i}} = 1$

[0075] For one-dimensional waves propagating, the compliance introducedby the pipe (in this case a circular tube of modulus E, radius R andwall thickness t) reduces the measured sound speed from the infinitedimensional sound speed. The effect of the conduit is given by thefollowing relationship:$\frac{1}{\rho_{mix}c_{measured}^{2}} = {{\frac{1}{\rho_{mix}c_{mix}^{2}} + {\sigma \quad {where}\quad \sigma}} \equiv \frac{2R}{Et}}$

[0076] Utilizing the relations above for a vapor/liquid mixture, thespeed at which sound travels within the representative vapor/liquidmixture is a function of vapor/liquid mass ratio. The effect ofincreasing liquid fraction, i.e. decreasing vapor/liquid ratio, isto-decrease the sound speed. Physically, adding liquid dropletseffectively mass loads the mixture, while not appreciably changing thecompressibility of the air. Over the parameter range of interest, therelation between mixture sound speed and vapor/liquid ratio is wellbehaved and monatomic.

[0077] While the calibration curves based on predictions from firstprinciples are encouraging, using empirical data mapping from soundspeed to vapor/liquid ratio may result in improved accuracy of thepresent invention to measure the vapor/liquid fractions of the mixture.

[0078] The sound speed increases with increasing frequency andasymptotes toward a constant value. The sound speed asymptote at higherfrequency is essentially the sound speed of air only with no influenceof the suspended liquid droplets. Also, it is apparent that the soundspeed of the vapor/liquid mixture has not reached the quasi-steady limitat the lowest frequency for which sound speed was measured. The soundspeed is continuing to decrease at the lower frequency limit. Animportant discovery of the present invention is that the speed at whichsound propagates through droplets suspended in a continuous vapor issaid to be dispersive. As defined herein, the speed at which acousticwaves propagate through dispersive mixtures varies with frequency.

[0079] Measuring the sound speed of a saturated vapor/liquid mixture 12at progressively lower and lower frequencies becomes inherently lessaccurate as the total length of the array of pressure sensors 115-118(Δx_(aperture)), which define the aperture of the array, becomes smallcompared to the wavelength of the acoustics. In general, the apertureshould be at least a significant fraction of a wavelength of the soundspeed of interest. Consequently, longer arrays are used to resolve soundspeeds at lower frequencies, which will be described in greater detailhereinafter. As shown in FIG. 14, the standard deviation associated withdetermining the speed of sound in air is shown as a function offrequency for three arrays of varying aperture, namely 1.5 ft, 3 ft and10 ft.

[0080] For accurately measuring sound speeds at ultra-low frequencies,the data suggests that utilizing a quasi-steady model to interpret therelationship between sound speed, measured at frequencies above those atwhich the quasi-steady model is applicable, and the liquid-to-vaporratio would be problematic, and may, in fact, be impractical. Thus, thekey to understanding and interpreting the composition of vapor/liquidmixtures through sound speed measurements lies in the dispersivecharacteristics of the vapor/liquid mixture, which is described ingreater detail in U.S. patent application Ser. No. 10/412,839, filedApr. 10, 2003; U.S. patent application Ser. No. 10/349,716, filed Jan.3, 2003; and U.S. patent application Ser. No. 10/376,427, filed Feb. 26,2003, which are all incorporated herein by reference.

[0081] In accordance with the present invention the dispersive nature ofthe system utilizes a first principles model of the interaction betweenthe vapor and liquid droplets. This model is viewed as beingrepresentative of a class of models that seek to account for dispersiveeffects. Other models could be used to account for dispersive effectswithout altering the intent of this disclosure (for example, see thepaper titled “Viscous Attenuation of Acoustic Waves in Suspensions” byR. L. Gibson, Jr. and M. N. Toksoz), which is incorporated herein byreference. The model allows for slip between the local velocity of thecontinuous vapor phase and that of the droplets. The drag force on thedroplets by the continuous vapor is modeled by a force proportional tothe difference between the local vapor velocity and that of the liquiddroplets and is balanced by inertial force:$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {\rho_{p}v_{p}\frac{\partial U_{p}}{\partial t}}}$

[0082] where K=proportionality constant, U_(f)=fluid velocity,U_(p)=liquid droplet velocity, ρ_(p)=liquid droplet density andv_(p)=particle volume.

[0083] The effect of the force on the continuous vapor phase by theliquid droplets is modeled as a force term in the axial momentumequation. The axial momentum equation for a control volume of area A andlength Δx is given by:${P_{x} - P_{x + {\Delta \quad x}} - {{K\left( {U_{f} - U_{p}} \right)}\left\{ \frac{\varphi_{p}\Delta \quad x}{v_{p}} \right\}}} = {\frac{\partial}{\partial t}\left( {\rho_{f}U_{f}\Delta \quad x} \right)}$

[0084] where P=pressure at locations x and Δx, φ_(p)=volume fraction ofthe liquid droplets, ρ_(f)=vapor density.

[0085] The droplet drag force is given by:$F_{drag} = {{K\left( {U_{f} - U_{p}} \right)} = {C_{d}A_{p}\frac{1}{2}{\rho_{f}\left( {U_{f} - U_{p}} \right)}^{2}}}$

[0086] where C_(d)=drag coefficient, A_(p)=frontal area of liquiddroplet and ρ_(f)=vapor density.

[0087] Using Stokes law for drag on a sphere at low Reynold's numbergives the drag coefficient as:$C_{d} = {\frac{24}{Re} = \frac{24\mu}{{\rho_{f}\left( {U_{f} - U_{p}} \right)}D_{p}}}$

[0088] where D_(p)=droplet diameter and μ=vapor viscosity.

[0089] Solving for K in this model yields:

K=3πμD _(p)

[0090] Using the above relations and 1-dimensional acoustic modelingtechniques, the following relation can be derived for the dispersivebehavior of an idealized vapor/liquid mixture.${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\phi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$

[0091] In the above relation, the fluid SOS, density (ρ) and viscosity(φ) are those of the pure phase fluid, v_(p) is the volume of individualdroplets and φ_(p) is the volumetric phase fraction of the droplets inthe mixture. These relationships to determine droplet size and liquid tovapor mass ratio are described in U.S. patent application Ser. No.10/412,839, filed Apr. 10, 2003; U.S. patent application Ser. No.10/349,716, filed Jan. 3, 2003; and U.S. patent application Ser. No.10/376,427, filed Feb. 26, 2003, which are all incorporated herein byreference.

[0092] The apparatus 10 further includes the ability to measure ofvolumetric flow rate of the mixture by comparing the difference of thespeed of one dimensional sound waves propagating with and against themean flow.

[0093] This method of determining the volumetric flow rate of the flow12 relies on the interaction of the mean flow with the acoustic pressurefield. The interaction results in sound waves propagating with the meanflow traveling at the speed of sound (if the vapor/liquid mixture werenot flowing) plus the convection velocity and, conversely, sound wavestraveling against the mean flow propagating at the speed of sound minusthe convection velocity. That is,

a _(R) =a _(mix) +u

a _(L) =a _(mix) −u

[0094] where a_(R)=velocity of a right traveling acoustic wave relativeto a stationary observer (i.e. the tube 14), a_(L)=velocity of a lefttraveling acoustic wave apparent to a stationary observer, a_(mix)=speedof sound traveling through the mixture (if the mixture was not flowing)and u=the mean flow velocity (assumed to be flowing from left to rightin this instance). Combining these two equations yields an equation forthe mean velocity, $u = \frac{a_{R} - a_{L}}{2}$

[0095] Therefore, by measuring the propagation velocity of acousticwaves in both directions relative to the pipe 14 as describedhereinbefore, the mean flow velocity can be calculated by multiplyingthe mean flow velocity by the cross-sectional area of the pipe 14.

[0096] The practicality of using this method to determine the mean flowis predicated on the ability to resolve the sound speed in bothdirections with sufficient accuracy to determine the volumetric flow.

[0097] For the sound speed measurement, the apparatus 10 utilizessimilar processing algorithms as those employed herein before, anddescribed in greater detail hereinafter. The temporal and spatialfrequency content of sound propagating within the pipe 14 is relatedthrough a dispersion relationship. $\omega = \frac{k}{a_{mix}}$

[0098] The wave number is k, which is defined as k=2π/λ, ω is thetemporal frequency in rad/sec, and a_(mix) is the speed at which soundpropagates within the process piping. For this cases where soundpropagates in both directions, the acoustic power is located along twoacoustic ridges, one for the sound traveling with the flow at a speed ofa_(mix)+V_(mix) and one for the sound traveling against the flow at aspeed of a_(mix)−V_(mix).

[0099] Further, FIG. 14 illustrates the ability of the present inventionto determine the velocity of a fluid moving in a pipe. The colorcontours represent the relative signal power at all combinations offrequency and wavenumber. The highest power “ridges” represent theacoustic wave with slope of the ridges equal to the propagation speed.Note that the acoustic ridges “wrap” to the opposite side of the plot atthe spatial Nyquist wavenumber equal to ±3.14 in this case (i.e. theacoustic ridge that slopes up and to the right starting at the bottom ofthe plot, the right-side ridge, wraps to the left side of the plot atapproximately 550 Hz and continues sloping up and to the right). Thedashed lines show the best-fit two-variable maximization of the powerwith the two variables being sound speed and flow velocity. Theright-side ridge represents the acoustic wave traveling in the samedirection as the bulk flow and therefore its slope is steeper than theleft-side ridge that represents the acoustic wave traveling in theopposite direction of the flow. This indicates that the acoustic wavetraveling in the same direction of the flow is traveling faster than theacoustic wave traveling in the opposite direction of the flow relativeto the stationary sensors located on the probe.

[0100] Referring to FIG. 1a, an apparatus 10 embodying the presentinvention includes the ability to measure volumetric flow rate of themixture by measuring the unsteady pressures generated by vorticaldisturbance propagating in the mixture. The apparatus 10 uses one orboth of the following techniques to determine the convection velocity ofthe vortical disturbances within the process flow 12 by:

[0101] 1) Cross-correlating unsteady pressure variations using an arrayof unsteady pressure sensors.

[0102] 2) Characterizing the convective ridge of the vorticaldisturbances using an array of unsteady pressure sensors.

[0103] The overwhelming majority of industrial process flows involveturbulent flow. Turbulent fluctuations within the process flow governmany of the flow properties of practical interest including the pressuredrop, heat transfer, and mixing. For engineering applications,considering only the time-averaged properties of turbulent flows isoften sufficient for design purposes. For sonar flow meteringtechnology, understanding the time-averaged velocity profile inturbulent flow provides a means to interpret the relationship betweenspeed at which coherent structures convect and the volumetricallyaveraged flow rate.

[0104] From the saturated vapor/liquid mixture mechanics perspective,this method relies on the ability of the apparatus 10 to isolate theconvective pressure field (which convects at or near the mean velocityof the saturated vapor/liquid mixture) from the acoustic pressure field(which propagates at the at the speed of sound). In this sense, thevelocity measurement is independent of the sound speed measurement.

[0105] For turbulent flows 12, the time-averaged axial velocity varieswith radial position from zero at the wall to a maximum at thecenterline of the pipe 14. The flow near the wall is characterized bysteep velocity gradients and transitions to relatively uniform core flownear the center of the pipe 14. FIG. 2 shows a representative schematicof a velocity profile and coherent vortical flow structures 188 presentin fully developed turbulent flow 12. The vortical structures 188 aresuperimposed over time averaged velocity profile within the pipe 14 andcontain temporally and spatially random fluctuations with magnitudestypically less than 10% percent of the mean flow velocity.

[0106] From a volumetric flow measurement perspective, thevolumetrically averaged flow velocity is of interest. The volumetricallyaveraged flow velocity, defined as V=Q/A, is a useful, but arbitrarilydefined property of the flow. Here, A is the cross sectional area of thetube and Q is the volumetric flow rate. In fact, given the velocityprofile within the tube, little flow is actually moving at this speed.

[0107] Turbulent pipe flows 12 are highly complex flows. Predicting thedetails of any turbulent flow is problematic, however, much is knownregarding the statistical properties of the flow. For instance,turbulent flows contain self-generating, coherent vortical structuresoften termed “turbulent eddies”. The maximum length scale of theseeddies is set by the diameter of the pipe 14. These structures remaincoherent for several tube diameters downstream, eventually breaking downinto progressively smaller eddies until the energy is dissipated byviscous effects.

[0108] Experimental investigations have established that eddiesgenerated within turbulent boundary layers convect at roughly 80% ofmaximum flow velocity. For tube flows, this implies that turbulenteddies will convect at approximately the volumetrically averaged flowvelocity within the pipe 14. The precise relationship between theconvection speed of turbulent eddies and the flow rate for each class ofmeters can be calibrated empirically as described below.

[0109] The apparatus 170 of FIG. 15 determines the convection velocityof the vortical disturbances within the flow by cross correlatingunsteady pressure variations using an array of unsteady pressuresensors, similar to that shown in U.S. patent application Ser. No.10/007,736, filed Nov. 8, 2001, entitled “Flow Rate Measurement UsingUnsteady Pressures”, which is incorporated herein by reference.

[0110] Referring to FIG. 15, the apparatus 170 includes a sensingsection 172 along a pipe 14 and a signal processing unit 174. The pipe14 has two measurement regions 176,178 located a distance ΔX apart alongthe pipe 14. At the first measurement region 176 are two unsteady (ordynamic or ac) pressure sensors 180,182, located a distance X₁ apart,capable of measuring the unsteady pressure in the pipe 14, and at thesecond measurement region 178, are two other unsteady pressure sensors84,86, located a distance X₂ apart, capable of measuring the unsteadypressure in the pipe 14. Each pair of pressure sensors 180,182 and184,186 act as spatial filters to remove certain acoustic signals fromthe unsteady pressure signals, and the distances X₁,X₂ are determined bythe desired filtering characteristic for each spatial filter, asdiscussed hereinafter.

[0111] The apparatus 170 of the present invention measures velocitiesassociated with unsteady flow fields and/or pressure disturbancesrepresented by 188 associated therewith relating to turbulent eddies (orvortical flow fields), inhomogeneities in the flow, or any otherproperties of the flow, liquid, vapor, or pressure, having time varyingor stochastic properties that are manifested at least in part in theform of unsteady pressures. The vortical flow fields are generatedwithin the flow of the pipe 14 by a variety of non-discrete sources suchas remote machinery, pumps, valves, elbows, as well as the fluid ormixture flow itself. It is this last source, the fluid flowing withinthe pipe, that is a generic source of vortical flow fields primarilycaused by the shear forces between the flow 12 and the wall of the tubethat assures a minimum level of disturbances for which the presentinvention takes unique advantage. The flow generated vortical flowfields generally increase with mean flow velocity and do not occur atany predeterminable frequency. As such, no external discretevortex-generating source is required within the present invention andthus may operate using passive detection. It is within the scope of thepresent that the pressure sensor spacing may be known or arbitrary andthat as few as two sensors are required if certain information is knownabout the acoustic properties of the system as will be more fullydescribed herein below.

[0112] The vortical flow fields 188 are, in general, comprised ofpressure disturbances having a wide variation in length scales and whichhave a variety of coherence length scales such as that described in thereference “Sound and Sources of Sound”, A. P. Dowling et al, HalstedPress, 1983, which is incorporated by reference to the extend ofunderstanding the invention. Certain of these vortical flow fields 188convect at or near, or related to the mean velocity of at least one ofthe elements within a mixture flowing through the pipe 14. The vorticalpressure disturbances 188 that contain information regarding convectionvelocity have temporal and spatial length scales as well as coherencelength scales that differ from other disturbances in the flow. Thepresent invention utilizes these properties to preferentially selectdisturbances of a desired axial length scale and coherence length scaleas will be more fully described hereinafter. For illustrative purposes,the terms vortical flow field and vortical pressure field will be usedto describe the above-described group of unsteady pressure fields havingtemporal and spatial length and coherence scales described herein.

[0113] Also, some or all of the functions within the signal processingunit 174 may be implemented in software (using a microprocessor orcomputer) and/or firmware, or may be implemented using analog and/ordigital hardware, having sufficient memory, interfaces, and capacity toperform the functions described herein.

[0114] In particular, in the processing unit 174, the pressure signalP₁(t) on the line 190 is provided to a positive input of a summer 200and the pressure signal P₂(t) on the line 191 is provided to a negativeinput of the summer 200. The output of the summer 200 is provided toline 204 indicative of the difference between the two pressure signalsP₁,P₂ (e.g., P₁−P₂=P_(as1)).

[0115] The pressure sensors 180,182 together with the summer 200 createa spatial filter 176. The line 204 is fed to bandpass filter 208, whichpasses a predetermined passband of frequencies and attenuatesfrequencies outside the passband. In accordance with the presentinvention, the passband of the filter 208 is set to filter out (orattenuate) the dc portion and the high frequency portion of the inputsignals and to pass the frequencies therebetween. Other passbands may beused in other embodiments, if desired. Passband filter 208 provides afiltered signal P_(asf) 1 on a line 212 to Cross-Correlation Logic 216,described hereinafter.

[0116] The pressure signal P₃(t) on the line 192 is provided to apositive input of a summer 202 and the pressure signal P₄(t) on the line193 is provided to a negative input of the summer 202. The pressuresensors 83,84 together with the summer 202 create a spatial filter 178.The output of the summer 202 is provided on a line 206 indicative of thedifference between the two pressure signals P₃,P₄(e.g., P₃−P₄=P_(as2)).The line 206 is fed to a bandpass filter 210, similar to the bandpassfilter 108 discussed hereinbefore, which passes frequencies within thepassband and attenuates frequencies outside the passband. The filter 210provides a filtered signal P_(asf) 2 on a line 214 to theCross-Correlation Logic 216. The signs on the summers 200,202 may beswapped if desired, provided the signs of both summers are swappedtogether. In addition, the pressure signals P₁,P₂,P₃,P₄ may be scaledprior to presentation to the summers 200,202.

[0117] The Cross-Correlation Logic 216 calculates a known time domaincross-correlation between the signals P_(asf1) and P_(asf2) on the lines212,214, respectively, and provides an output signal on a line 218indicative of the time delay τ it takes for an vortical flow field 188(or vortex, stochastic, or vortical structure, field, disturbance orperturbation within the flow) to propagate from one sensing region 176to the other sensing region 178. Such vortical flow disturbances, as isknown, are coherent dynamic conditions that can occur in the flow whichsubstantially decay (by a predetermined amount) over a predetermineddistance (or coherence length) and convect (or flow) at or near theaverage velocity of the fluid flow. As described above, the vorticalflow field 188 also has a stochastic or vortical pressure disturbanceassociated with it. In general, the vortical flow disturbances 188 aredistributed throughout the flow, particularly in high shear regions,such as boundary layers (e.g., along the inner wall of the tube 14) andare shown herein as discrete vortical flow fields 188. Because thevortical flow fields (and the associated pressure disturbance) convectat or near the mean flow velocity, the propagation time delay τ isrelated to the velocity of the flow by the distance ΔX between themeasurement regions 176,178, as discussed hereinafter.

[0118] Referring to FIG. 15, a spacing signal ΔX on a line 220indicative of the distance ΔX between the sensing regions 176,178 isdivided by the time delay signal τ on the line 218 by a divider 222which provides an output signal on the line 196 indicative of theconvection velocity U_(c)(t) of the saturated vapor/liquid mixtureflowing in the pipe 14, which is related to (or proportional to orapproximately equal to) the average (or mean) flow velocity U_(f)(t) ofthe flow 12, as defined below:

U _(c)(t)=ΔX/τ∝U _(f)(t)  Eq. 1

[0119] The present invention uses temporal and spatial filtering toprecondition the pressure signals to effectively filter out the acousticpressure disturbances P_(acoustic) and other long wavelength (comparedto the sensor spacing) pressure disturbances in the tube 14 at the twosensing regions 176,178 and retain a substantial portion of the vorticalpressure disturbances P_(vortical) associated with the vortical flowfield 188 and any other short wavelength (compared to the sensorspacing) low frequency pressure disturbances P_(other). In accordancewith the present invention, if the low frequency pressure disturbancesP_(other) are small, they will not substantially impair the measurementaccuracy of P_(vortical).

[0120] The second technique of determining the convection velocity ofthe vortical disturbances within the flow 12 is by characterizing theconvective ridge of the vortical disturbances using an array of unsteadypressure sensors, similar to that shown in U.S. patent application Ser.No. 09/729,994, filed Dec. 4, 2000, entitled “Method and Apparatus forDetermining the Flow Velocity Within a Pipe”, which is incorporatedherein by reference.

[0121] The sonar flow metering methodology uses the convection velocityof coherent structure with turbulent pipe flows 12 to determine thevolumetric flow rate. The convection velocity of these eddies 188 isdetermined by applying sonar arraying processing techniques to determinethe speed at which the eddies convect past an axial array of unsteadypressure measurements distributed along the pipe 14.

[0122] The sonar-based algorithms determine the speed of the eddies 188by characterizing both the temporal and spatially frequencycharacteristics of the flow field. For a train of coherent eddiesconvecting past a fixed array of sensors, the temporal and spatialfrequency content of pressure fluctuations are related through thefollowing relationship: $\omega = \frac{k}{U_{convect}}$

[0123] Here k is the wave number, defined as k=2π/λ and has units of1/length, ω is the temporal frequency in rad/sec, and U_(convect) is theconvection velocity. Thus, the shorter the wavelength (larger k) is, thehigher the temporal frequency.

[0124] In sonar array processing, the spatial/temporal frequency contentof time stationary sound fields are often displayed using “k-ω plots”.K-ω plots are essentially three-dimensional power spectra in which thepower of a sound field is decomposed into bins corresponding to specificspatial wave numbers and temporal frequencies. On a k-ω plot, the powerassociated with a pressure field convecting with the flow is distributedin regions, which satisfies the dispersion relationship developed above.This region is termed “the convective ridge” (Beranek, 1992) and theslope of this ridge on a k-w plot indicates the convective velocity ofthe pressure field. This suggests that the convective velocity ofturbulent eddies, and hence flow rate within a tube, can be determinedby constructing a k-ω plot from the output of a phased array of sensorand identifying the slope of the convective ridge.

[0125]FIG. 16 shows an example of a k-ω plot generated from a phasedarray of pressure sensors. The power contours show a well-definedconvective ridge. A parametric optimization method was used to determinethe “best” line representing the slope of the convective ridge 200. Forthis case, a slope of 14.2 ft/sec was determined. The intermediateresult of the optimization procedure is displayed in the insert, showingthat optimized value is a unique and well-defined optima.

[0126] The k-w plot shown in FIG. 16 illustrates the fundamentalprinciple behind sonar based flow measure, namely that axial arrays ofpressure sensors can be used in conjunction with sonar processingtechniques to determine the speed at which naturally occurring turbulenteddies convect within a pipe.

[0127] The present invention will now be described with reference toFIG. 17 wherein the discussions based on the calculation of variousparameters and properties are detailed herein above with reference tothe various Figures. In accordance with the present invention utilizinga probe 10,110,170 to determine the speed of sound propagating through aflow 12, such as a mixture, provides various specific properties of amixture and the velocity of the mixture and further utilizing logiccomprising information about the flow 12 based on the measuredparameters. The steady state pressure and temperature of the mixture maybe measured by any known or contemplated method as represented by 270from which various fluid properties may be determined from tables orgraphs of the known relationships for speed of sound and density for thetwo phases of the mixture as represented by 271. The speed of soundpropagating through the mixture is determined by the apparatus10,110,170 of the present invention as set forth herein above andrepresented by 272. The quality of the saturated vapor/liquid mixture isdetermined from the fluid properties of 271 combined with the mixturespeed of sound 272 using the Wood equation (or similar) as set forthherein above and represented by 273. The present invention also enablesthe determination of other properties of the mixture such as enthalpyand density as set forth by 274 by combining the fluid properties of 271with the quality or composition of the mixture from 273. The presentinvention further enables the determination of the velocity of themixture by the methods described herein above as represented by 275. Thetotal volumetric flow rate of the mixture is thereby determined asrepresented by 276 and when combined with the parameters of otherproperties of the mixture such as enthalpy and density as set forth by274 various flux rates of the mixture such as enthalpy and mass flowrates are enabled as represented by 277.

[0128] Another embodiment of the present invention include a pressuresensor such as pipe strain sensors, accelerometers, velocity sensors ordisplacement sensors, discussed hereinafter, that are mounted onto astrap to enable the pressure sensor to be clamped onto the pipe. Thesensors may be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. These certain typesof pressure sensors, it may be desirable for the pipe 12 to exhibit acertain amount of pipe compliance.

[0129] Instead of single point pressure sensors 18-21, at the axiallocations along the pipe 12, two or more pressure sensors may be usedaround the circumference of the pipe 12 at each of the axial locations.The signals from the pressure sensors around the circumference at agiven axial location may be averaged to provide a cross-sectional (orcircumference) averaged unsteady acoustic pressure measurement. Othernumbers of acoustic pressure sensors and annular spacing may be used.Averaging multiple annular pressure sensors reduces noises fromdisturbances and pipe vibrations and other sources of noise not relatedto the one-dimensional acoustic pressure waves in the pipe 12, therebycreating a spatial array of pressure sensors to help characterize theone-dimensional sound field within the pipe 12.

[0130] The pressure sensors 18-21 of FIG. 1a described herein may be anytype of pressure sensor, capable of measuring the unsteady (or ac ordynamic) pressures within a pipe 14, such as piezoelectric, optical,capacitive, resistive (e.g., Wheatstone bridge), accelerometers (orgeophones), velocity measuring devices, displacement measuring devices,etc. If optical pressure sensors are used, the sensors 18-21 may beBragg grating based pressure sensors, such as that described in U.S.patent application, Ser. No. 08/925,598, entitled “High SensitivityFiber Optic Pressure Sensor For Use In Harsh Environments”, filed Sept.8, 1997, now U.S. Pat. No. 6,016,702, and in U.S. patent application,Ser. No. 10/224,821, entitled “Non-Intrusive Fiber Optic Pressure Sensorfor Measuring Unsteady Pressures within a Pipe”, which are incorporatedherein by reference. In an embodiment of the present invention thatutilizes fiber optics as the pressure sensors 14 they may be connectedindividually or may be multiplexed along one or more optical fibersusing wavelength division multiplexing (WDM), time division multiplexing(TDM), or any other optical multiplexing techniques.

[0131] It is also within the scope of the present invention that anyother strain sensing technique may be used to measure the variations instrain in the tube, such as highly sensitive piezoelectric, electronicor electric, strain gages attached to or embedded in the tube 14.

[0132] In certain embodiments of the present invention, apiezo-electronic pressure transducer may be used as one or more of thepressure sensors 15-18 and it may measure the unsteady (or dynamic orac) pressure variations inside the tube 14 by measuring the pressurelevels inside of the tube. In an embodiment of the present invention,the sensors 14 comprise pressure sensors manufactured by PCBPiezotronics. In one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

[0133] The pressure sensors incorporate a built-in MOSFETmicroelectronic amplifier to convert the high-impedance charge outputinto a low-impedance voltage signal. The sensor is powered from aconstant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply. A data acquisition system ofthe present invention may incorporate constant-current power fordirectly powering integrated circuit piezoelectric sensors.

[0134] Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

[0135] The output characteristic of piezoelectric pressure sensorsystems is that of an AC-coupled system, where repetitive signals decayuntil there is an equal area above and below the original base line. Asmagnitude levels of the monitored event fluctuate, the output remainsstabilized around the base line with the positive and negative areas ofthe curve remaining equal.

[0136] It is also within the scope of the present invention that anystrain sensing technique may be used to measure the variations in strainin the pipe, such as highly sensitive piezoelectric, electronic orelectric, strain gages and piezo-resistive strain gages attached to thepipe 12. Other strain gages include resistive foil type gages having arace track configuration similar to that disclosed U.S. patentapplication Ser. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No.6,354,147, which is incorporated herein by reference. The invention alsocontemplates strain gages being disposed about a predetermined portionof the circumference of pipe 12. The axial placement of and separationdistance ΔX₁, ΔX₂ between the strain sensors are determined as describedherein above.

[0137] It should be understood that any of the features,characteristics, alternatives or modifications described regarding aparticular embodiment herein may also be applied, used, or incorporatedwith any other embodiment described herein.

[0138] Although the invention has been described and illustrated withrespect to exemplary embodiments thereof, the foregoing and variousother additions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

What is claimed is:
 1. An apparatus for measuring at least one parameterof a process flow flowing within a pipe, the apparatus comprising: atleast two pressure sensors clamped onto the outer surface of the pipe atdifferent axial locations along the pipe, each of the pressure sensorsproviding a respective pressure signal indicative of a pressuredisturbance within the pipe at a corresponding axial position, each ofthe pressure sensors comprising a piezoelectric film sensor; and asignal processor, responsive to said pressure signals, which provides asignal indicative of at least one parameter of the process flow flowingwithin the pipe.
 2. The apparatus of claim 1, wherein each of thepressure sensors further include a strap for attaching the piezoelectricfilm sensor thereto.
 3. The apparatus of claim 1, wherein the processflow is one of a single phase fluid and a multi-phase mixture.
 4. Theapparatus of claim 2, wherein the piezoelectric film sensor is attachedto the outer surface of the strap and/or the inner surface of the strap.5. The apparatus of claim 2, wherein the strap is a metallic material.6. The apparatus of claim 2, further includes a clamping device forattaching the ends of one of the pressure sensors to clamp the pressuresensor onto the pipe.
 7. The apparatus of claim 2, wherein the pressuresensors are removably clamped to the pipe.
 8. The apparatus of claim 2,wherein the pressure sensors are permanently clamped to the pipe.
 9. Theapparatus of claim 1, wherein the piezoelectric film sensor includes atleast one of polyvinylchlorine fluoride (PDVF), polymer film andflexible PZT.
 10. The apparatus of claim 1, wherein the piezoelectricfilm includes a pair of conductors disposed on opposing surfaces of thepiezoelectric-film.
 11. The apparatus of claim 10, wherein each the pairof conductors is a coating of silver ink.
 12. The apparatus of claim 1,wherein the piezoelectric film extends around a substantial portion ofthe circumference of the pipe.
 13. The apparatus of claim 1, wherein thepiezoelectric film has a thickness greater than 8 mm.
 14. The apparatusof claim 1, wherein the piezoelectric film has a thickness between 8 mmand 120 mm.
 15. The apparatus of claim 1, further includes an electricalinsulator between the piezoelectric film and the strap.
 16. Theapparatus of claim 1, wherein the pressure signals are indication ofacoustic pressures propagating within the pipe.
 17. The apparatus ofclaim 1, wherein the parameter of the fluid is one of steam quality or“wetness”, vapor/mass ratio, liquid/solid ratio, volumetric flow rate,mass flow rate, size of suspended particles, density, gas volumefraction, and enthalpy of the flow.
 18. The apparatus of claim 1,wherein the signal processor determines the slope of an acoustic ridgein the k-w plane to determine a parameter of the process flow flowing inthe pipe.
 19. The apparatus of claim 1, wherein the pressure signals areindication of vortical disturbances within the fluid flow.
 20. Theapparatus of claim 19, wherein the parameter of the fluid is one ofvelocity of the process flow and the volumetric flow of the processfluid.
 21. The apparatus of claim 1, wherein the signal processordetermines the slope of a convective ridge in the k-w plane to determinethe velocity of the fluid flowing in the pipe.
 22. The apparatus ofclaim 1, wherein the signal processor determines the volumetric flowrate of the fluid flowing in the pipe in response to the velocity of thefluid.
 23. The apparatus of claim 1, wherein the signal processorgenerates a flow velocity signal indicative of the velocity of the fluidflowing within the pipe by cross-correlating the pressure signals. 24.The apparatus of claim 1 wherein each sensor measures an acousticpressure and provides a signal indicative of an acoustic noise withinthe pipe.
 25. The apparatus of claim 1 further comprising at least threeof said pressure sensors.
 26. The apparatus of claim 1, wherein thepressure sensors are mounted to the outer surface of the pipe.
 27. Theapparatus of claim 26, wherein the pressure sensors are mounted to theouter surface of the pipe by an adhesive.